formula.cpp

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/*
   Copyright (C) 2003 - 2018 by David White <dave@whitevine.net>
   Part of the Battle for Wesnoth Project https://www.wesnoth.org/

   This program is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation; either version 2 of the License, or
   (at your option) any later version.
   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY.

   See the COPYING file for more details.
*/

#include "formula/formula.hpp"

#include "formula/callable.hpp"
#include "formula/function.hpp"
#include "formula/string_utils.hpp"
#include "random.hpp"
#include "serialization/string_utils.hpp"
#include "log.hpp"

#include <cassert>
#include <set>
#include <sstream>

// This is here only for the below initialization code.
// If other logging is required in this file, it should use a different logdomain
// (probably "scripting/formula" or something)
static lg::log_domain log_engine("engine");
#define ERR_NG LOG_STREAM(err, log_engine)

namespace utils {
    namespace detail {
        std::string evaluate_formula_impl(const std::string&);

        std::string evaluate_formula_impl(const std::string& formula) {
            try {
                const wfl::formula form(formula);
                return form.evaluate().string_cast();
            } catch(const wfl::formula_error& e) {
                ERR_NG << "Formula in WML string cannot be evaluated due to "
                    << e.type << "\n\t--> \"";
                return "";
            }
        }

        struct formula_initer {
            formula_initer() {
                evaluate_formula = &evaluate_formula_impl;
            }
        } init;
    }
}

namespace wfl
{
using expr_table           = std::map<std::string, expression_ptr>;
using expr_table_evaluated = std::map<std::string, variant>;
using expr_table_ptr       = std::shared_ptr<expr_table>;

// Function used when creating error reports.
// Parses all tokens passed to parse_expression, thus there are no EOL or whitespaces
static std::string tokens_to_string(const tk::token* i1, const tk::token* i2)
{
    std::ostringstream expr;
    while(i1 != i2) {
        expr << std::string(i1->begin, i1->end) << " ";
        ++i1;
    }

    return expr.str();
}

class null_expression : public formula_expression
{
public:
    null_expression() {}

    std::string str() const
    {
        return "";
    }

private:
    variant execute(const formula_callable& /*variables*/, formula_debugger* /*fdb*/) const
    {
        return variant();
    }
};

// Implemented further down
expression_ptr parse_expression(const tk::token* i1, const tk::token* i2, function_symbol_table* symbols);


const char* const formula::id_chars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ_";

formula::formula(const std::string& text, function_symbol_table* symbols)
    : expr_()
    , str_(text)
    , managed_symbols_(symbols ? nullptr : new function_symbol_table)
    , symbols_(symbols ? symbols : managed_symbols_.get())
{
    std::vector<tk::token> tokens;
    std::string::const_iterator i1 = text.begin(), i2 = text.end();

    // Set true when 'fai' keyword is found
    bool fai_keyword = false;

    // Set true when 'wfl' keyword is found
    bool wfl_keyword = false;

    // Used to locally keep the track of which file we parse actually and in which line we are
    std::vector<std::pair<std::string, int>> files;

    // Used as a source of strings - we point to these strings from tokens
    std::set<std::string> filenames;

    files.emplace_back("formula", 1);
    filenames.insert("formula");

    std::set<std::string>::iterator filenames_it = filenames.begin();

    while(i1 != i2) {
        try {
            tokens.push_back(tk::get_token(i1,i2));

            tk::TOKEN_TYPE current_type = tokens.back().type;

            if(current_type == tk::TOKEN_WHITESPACE)  {
                tokens.pop_back();
            } else if(current_type == tk::TOKEN_COMMENT) {
                // Since we can have multiline comments, let's see how many EOL are within it
                int counter = 0;

                std::string comment = std::string(tokens.back().begin, tokens.back().end);
                for(const auto& str_it : comment) {
                    if(str_it == '\n') {
                        counter++;
                    }
                }

                files.back().second += counter;
                tokens.pop_back();
            } else if(current_type == tk::TOKEN_EOL) {
                files.back().second++;
                tokens.pop_back();
            } else if((current_type == tk::TOKEN_KEYWORD) && (std::string(tokens.back().begin, tokens.back().end) == "fai")) {
                fai_keyword = true;
                tokens.pop_back();
            } else if((current_type == tk::TOKEN_KEYWORD) && (std::string(tokens.back().begin, tokens.back().end) == "wfl")) {
                wfl_keyword = true;
                tokens.pop_back();
            } else if((current_type == tk::TOKEN_KEYWORD) && (std::string(tokens.back().begin, tokens.back().end) == "faiend")) {
                if(files.size() > 1) {
                    files.pop_back();
                    filenames_it = filenames.find(files.back().first);

                    tokens.pop_back();
                } else {
                    throw formula_error("Unexpected 'faiend' found", "", "", 0);
                }
            } else if((current_type == tk::TOKEN_KEYWORD) && (std::string(tokens.back().begin, tokens.back().end) == "wflend")) {
                if(files.size() > 1) {
                    files.pop_back();
                    filenames_it = filenames.find(files.back().first);

                    tokens.pop_back();
                } else {
                    throw formula_error("Unexpected 'wflend' found", "", "", 0);
                }
            } else if(fai_keyword || wfl_keyword) {
                if(current_type == tk::TOKEN_STRING_LITERAL) {
                    std::string str = std::string(tokens.back().begin, tokens.back().end);
                    files.emplace_back(str , 1);

                    auto [pos, success] = filenames.insert(str);

                    if(success) {
                        filenames_it = pos;
                    } else {
                        if(fai_keyword) {
                            throw formula_error("Faifile already included", "fai" + str, "", 0);
                        } else {
                            throw formula_error("Wflfile already included", "wfl" + str, "", 0);
                        }
                    }

                    tokens.pop_back();
                    fai_keyword = false;
                    wfl_keyword = false;
                } else {
                    if(fai_keyword) {
                        throw formula_error("Expected string after the 'fai'", "fai", "", 0);
                    } else {
                        throw formula_error("Expected string after the 'wfl'", "wfl", "", 0);
                    }
                }
            } else {
                // In every token not specified above, store line number and name of file it came from
                tokens.back().filename = &(*filenames_it);
                tokens.back().line_number = files.back().second;
            }
        } catch(const tk::token_error& e) {
            // When we catch token error, we should write whole line in which error occurred,
            // so we merge info from token and everything we had in the line so far
            std::string str = "";
            if(!tokens.empty()) {
                tk::token* tok_it = &tokens[0] + tokens.size()-1;
                while(( tok_it != &tokens[0] ) && (tok_it->line_number == tokens.back().line_number)) {
                    --tok_it;
                }

                if(tok_it != &tokens[0] && tok_it != &tokens[0] + tokens.size() -1) {
                    ++tok_it;
                }

                str = tokens_to_string(tok_it, &tokens[0] + tokens.size());
            }

            throw formula_error(e.description_, str + e.formula_, *filenames_it, files.back().second);
        }
    }

    if(files.size() > 1) {
        throw formula_error("Missing 'wflend', make sure each .wfl file ends with it", "", "", 0);
    }

    if(!tokens.empty()) {
        expr_ = parse_expression(&tokens[0], &tokens[0] + tokens.size(), symbols_);
    } else {
        expr_ = std::make_shared<null_expression>();
    }
}

formula::formula(const tk::token* i1, const tk::token* i2, function_symbol_table* symbols)
    : expr_()
    , str_()
    , managed_symbols_(symbols ? nullptr : new function_symbol_table)
    , symbols_(symbols ? symbols : managed_symbols_.get())
{
    if(i1 != i2) {
        expr_ = parse_expression(i1, i2, symbols);
    } else {
        expr_ = std::make_shared<null_expression>();
    }
}

formula_ptr formula::create_optional_formula(const std::string& str, function_symbol_table* symbols)
{
    if(str.empty()) {
        return formula_ptr();
    }

    return formula_ptr(new formula(str, symbols));
}

variant formula::execute(const formula_callable& variables, formula_debugger*fdb) const
{
    try {
        return expr_->evaluate(variables, fdb);
    } catch(const type_error& e) {
        std::cerr << "formula type error: " << e.message << "\n";
        return variant();
    }
}

variant formula::execute(formula_debugger*fdb) const
{
    static map_formula_callable null_callable;
    return execute(null_callable,fdb);
}


formula_error::formula_error(const std::string& type, const std::string& formula,
        const std::string& file, int line)
    : error()
    , type(type)
    , formula(formula)
    , filename(file)
    , line(line)
{
    std::stringstream ss;
    ss << "Formula error in " << filename << ":" << line
       << "\nIn formula " << formula
       << "\nError: " << type;
    message = ss.str();
}


/**
 * Classes that encapsulate and handle the various formula functions.
 */
class function_list_expression : public formula_expression
{
public:
    explicit function_list_expression(function_symbol_table* symbols)
        : symbols_(symbols)
    {}

    virtual std::string str() const
    {
        return "{function_list_expression()}";
    }

private:
    variant execute(const formula_callable& /*variables*/, formula_debugger* /*fdb*/) const
    {
        std::vector<variant> res;
        for(const std::string& fcn_name : symbols_->get_function_names()) {
            res.emplace_back(fcn_name);
        }

        return variant(res);
    }

    function_symbol_table* symbols_;
};

class list_expression : public formula_expression
{
public:
    explicit list_expression(const std::vector<expression_ptr>& items)
        : items_(items)
    {}

private:
    variant execute(const formula_callable& variables, formula_debugger*fdb) const
    {
        std::vector<variant> res;
        res.reserve(items_.size());
        for(const auto& i : items_) {
            res.push_back(i->evaluate(variables, add_debug_info(fdb, 0, "[list element]")));
        }

        return variant(res);
    }

    std::vector<expression_ptr> items_;

    std::string str() const
    {
        std::stringstream s;
        s << '[';
        bool first_item = true;
        for(expression_ptr a : items_) {
            if(!first_item) {
                s << ',';
            } else {
                first_item = false;
            }
            s << a->str();
        }
        s << ']';
        return s.str();
    }
};

class map_expression : public formula_expression
{
public:
    explicit map_expression(const std::vector<expression_ptr>& items)
        : items_(items)
    {}

    virtual std::string str() const
    {
        std::stringstream s;
        s << " [";
        for(std::vector<expression_ptr>::const_iterator i = items_.begin(); (i != items_.end()) && (i + 1 != items_.end()) ; i += 2) {
            if(i != items_.begin()) {
                s << ", ";
            }
            s << (*i)->str();
            s << " -> ";
            s << (*(i+1))->str();
        }
        if(items_.empty()) {
            s << "->";
        }
        s << " ]";
        return s.str();
    }

private:
    variant execute(const formula_callable& variables, formula_debugger*fdb) const
    {
        std::map<variant,variant> res;
        for(std::vector<expression_ptr>::const_iterator i = items_.begin(); (i != items_.end()) && (i + 1 != items_.end()) ; i += 2) {
            variant key = (*i)->evaluate(variables, add_debug_info(fdb, 0, "key ->"));
            variant value = (*(i+1))->evaluate(variables, add_debug_info(fdb, 1, "-> value"));
            res[key] = value;
        }

        return variant(res);
    }

    std::vector<expression_ptr> items_;
};

class unary_operator_expression : public formula_expression
{
public:
    unary_operator_expression(const std::string& op, expression_ptr arg)
        : op_(),op_str_(op)
        , operand_(arg)
    {
        if(op == "not") {
            op_ = NOT;
        } else if(op == "-") {
            op_ = SUB;
        } else {
            throw formula_error("Illegal unary operator: '" + op + "'" , "", "", 0);
        }
    }

    virtual std::string str() const
    {
        std::stringstream s;
        s << op_str_ << '('<< operand_->str() << ')';
        return s.str();
    }

private:
    variant execute(const formula_callable& variables, formula_debugger*fdb) const
    {
        const variant res = operand_->evaluate(variables, add_debug_info(fdb, 0, op_str_ + " unary"));
        switch(op_) {
        case NOT:
            return res.as_bool() ? variant(0) : variant(1);
        case SUB:
        default:
            return -res;
        }
    }

    enum OP { NOT, SUB };
    OP op_;
    std::string op_str_;
    expression_ptr operand_;
};

class string_callable : public formula_callable
{
public:
    explicit string_callable(const variant& string) : string_(string) {}

    void get_inputs(formula_input_vector& inputs) const
    {
        add_input(inputs, "size");
        add_input(inputs, "empty");
        add_input(inputs, "char");
        add_input(inputs, "word");
        add_input(inputs, "item");
    }

    variant get_value(const std::string& key) const
    {
        if(key == "size") {
            return variant(string_.as_string().length());
        } else if(key == "empty") {
            return variant(string_.as_string().empty());
        } else if(key == "char" || key == "chars") {
            std::vector<variant> chars;
            for(char c : string_.as_string()) {
                chars.emplace_back(std::string(1, c));
            }

            return variant(chars);
        } else if(key == "word" || key == "words") {
            std::vector<variant> words;
            const std::string& str = string_.as_string();
            std::size_t next_space = 0;
            do {
                std::size_t last_space = next_space;
                next_space = str.find_first_of(" \t", next_space);
                words.emplace_back(str.substr(last_space, next_space - last_space));
                next_space = str.find_first_not_of(" \t", next_space);
            } while(next_space != std::string::npos);

            return variant(words);
        } else if(key == "item" || key == "items") {
            std::vector<std::string> split = utils::parenthetical_split(string_.as_string(), ',');
            std::vector<variant> items;
            items.reserve(split.size());
            for(const std::string& s : split) {
                items.emplace_back(s);
            }

            return variant(items);
        }

        return variant();
    }

private:
    variant string_;
};

class list_callable : public formula_callable
{
public:
    explicit list_callable(const variant& list) : list_(list) {}

    void get_inputs(formula_input_vector& inputs) const
    {
        add_input(inputs, "size", FORMULA_READ_WRITE);
        add_input(inputs, "empty", FORMULA_READ_WRITE);
        add_input(inputs, "first", FORMULA_READ_WRITE);
        add_input(inputs, "last", FORMULA_READ_WRITE);
    }

    variant get_value(const std::string& key) const
    {
        if(key == "size") {
            return variant(list_.num_elements());
        } else if(key == "empty") {
            return variant(list_.num_elements() == 0);
        } else if(key == "first") {
            if(list_.num_elements() > 0) {
                return list_[0];
            }

            return variant();
        } else if(key == "last") {
            if(list_.num_elements() > 0) {
                return list_[list_.num_elements()-1];
            }

            return variant();
        }

        return variant();
    }

private:
    variant list_;
};

class map_callable : public formula_callable
{
public:
    explicit map_callable(const variant& map) : map_(map) {}

    void get_inputs(formula_input_vector& inputs) const
    {
        add_input(inputs, "size", FORMULA_READ_WRITE);
        add_input(inputs, "empty", FORMULA_READ_WRITE);

        for(const auto& v : map_) {
            // variant_iterator does not implement operator->,
            // and to do so is notrivial since it returns temporaries for maps.
            const variant& key_variant = v.get_member("key");
            if(!key_variant.is_string()) {
                continue;
            }

            std::string key = key_variant.as_string();
            bool valid = true;
            for(char c : key) {
                if(!isalpha(c) && c != '_') {
                    valid = false;
                    break;
                }
            }

            if(valid) {
                add_input(inputs, key);
            }
        }
    }

    variant get_value(const std::string& key) const
    {
        const variant key_variant(key);
        if(map_.as_map().find(key_variant) != map_.as_map().end()) {
            return map_[key_variant];
        } else if(key == "size") {
            return variant(map_.num_elements());
        } else if(key == "empty") {
            return variant(map_.num_elements() == 0);
        }

        return variant();
    }

private:
    variant map_;
};

class dot_callable : public formula_callable
{
public:
    dot_callable(const formula_callable &global, const formula_callable& local)
        : global_(global), local_(local)
    {}

private:
    const formula_callable& global_, &local_;

    void get_inputs(formula_input_vector& inputs) const
    {
        return local_.get_inputs(inputs);
    }

    variant get_value(const std::string& key) const
    {
        variant v = local_.query_value(key);

        if( v == variant() )
            return global_.query_value(key);
        else
            return v;
    }
};

class dot_expression : public formula_expression
{
public:
    dot_expression(expression_ptr left, expression_ptr right)
        : left_(left), right_(right)
    {}

    std::string str() const
    {
        std::stringstream s;
        s << left_->str() << "." << right_->str();
        return s.str();
    }

private:
    variant execute(const formula_callable& variables, formula_debugger*fdb) const
    {
        const variant left = left_->evaluate(variables, add_debug_info(fdb,0,"left ."));
        if(!left.is_callable()) {
            if(left.is_list()) {
                list_callable list_call(left);
                dot_callable callable(variables, list_call);
                return right_->evaluate(callable,fdb);
            }

            if(left.is_map()) {
                map_callable map_call(left);
                dot_callable callable(variables, map_call);
                return right_->evaluate(callable,fdb);
            }

            if(left.is_string()) {
                string_callable string_call(left);
                dot_callable callable(variables, string_call);
                return right_->evaluate(callable,fdb);
            }

            return left;
        }

        dot_callable callable(variables, *left.as_callable());
        return right_->evaluate(callable, add_debug_info(fdb,1,". right"));
    }

    expression_ptr left_, right_;
};

class square_bracket_expression : public formula_expression
{
public:
    square_bracket_expression(expression_ptr left, expression_ptr key)
        : left_(left), key_(key)
    {}

    std::string str() const
    {
        std::stringstream s;
        s << left_->str() << '[' << key_->str() << ']';
        return s.str();
    }

private:
    variant execute(const formula_callable& variables, formula_debugger*fdb) const
    {
        const variant left = left_->evaluate(variables, add_debug_info(fdb,0,"base[]"));
        const variant key = key_->evaluate(variables, add_debug_info(fdb,1,"[index]"));
        if(left.is_list() || left.is_map()) {
            return left[key];
        }

        return variant();
    }

    expression_ptr left_, key_;
};

class operator_expression : public formula_expression
{
public:
    operator_expression(const std::string& op, expression_ptr left, expression_ptr right)
        : op_(OP(op[0])), op_str_(op), left_(left), right_(right)
    {
        if(op == ">=") {
            op_ = GTE;
        } else if(op == "<=") {
            op_ = LTE;
        } else if(op == "!=") {
            op_ = NEQ;
        } else if(op == "and") {
            op_ = AND;
        } else if(op == "or") {
            op_ = OR;
        } else if(op == ".+") {
            op_ = ADDL;
        } else if(op == ".-") {
            op_ = SUBL;
        } else if(op == ".*") {
            op_ = MULL;
        } else if(op == "./") {
            op_ = DIVL;
        } else if(op == "..") {
            op_ = OP_CAT;
        } else if(op == "in") {
            op_ = OP_IN;
        }
    }

    std::string str() const
    {
        std::stringstream s;
        s << '(' << left_->str() << op_str_ << right_->str() << ')';
        return s.str();
    }

private:
    variant execute(const formula_callable& variables, formula_debugger*fdb) const
    {
        const variant left = left_->evaluate(variables, add_debug_info(fdb, 0, "left " + op_str_));
        const variant right = right_->evaluate(variables, add_debug_info(fdb, 1, op_str_ + " right"));

        switch(op_) {
        case AND:
            return left.as_bool() == false ? left : right;
        case OR:
            return left.as_bool() ? left : right;
        case ADD:
            return left + right;
        case SUB:
            return left - right;
        case MUL:
            return left * right;
        case DIV:
            return left / right;
        case POW:
            return left ^ right;
        case ADDL:
            return left.list_elements_add(right);
        case SUBL:
            return left.list_elements_sub(right);
        case MULL:
            return left.list_elements_mul(right);
        case DIVL:
            return left.list_elements_div(right);
        case OP_IN:
            return variant(right.contains(left));
        case OP_CAT:
            return left.concatenate(right);
        case EQ:
            return left == right ? variant(1) : variant(0);
        case NEQ:
            return left != right ? variant(1) : variant(0);
        case LTE:
            return left <= right ? variant(1) : variant(0);
        case GTE:
            return left >= right ? variant(1) : variant(0);
        case LT:
            return left < right ? variant(1) : variant(0);
        case GT:
            return left > right ? variant(1) : variant(0);
        case MOD:
            return left % right;
        case RAN:
            return left.build_range(right);
        case DICE:
            return variant(dice_roll(left.as_int(), right.as_int()));
        default:
            std::cerr << "ERROR: Unimplemented operator!" << std::endl;
            return variant();
        }
    }

    static int dice_roll(int num_rolls, int faces)
    {
        int res = 0;
        while(faces > 0 && num_rolls-- > 0) {
            res += randomness::generator->get_random_int(1, faces);
        }

        return res;
    }

    //In some cases a IN  or CAT macros are defined.
    enum OP { AND, OR, NEQ, LTE, GTE, OP_CAT, OP_IN, GT='>', LT='<', EQ='=', RAN='~',
              ADD='+', SUB='-', MUL='*', DIV='/', ADDL, SUBL, MULL, DIVL, DICE='d', POW='^', MOD='%' };

    OP op_;
    std::string op_str_;
    expression_ptr left_, right_;
};

class where_variables: public formula_callable
{
public:
    where_variables(const formula_callable &base, expr_table_ptr table, formula_debugger* fdb)
        : formula_callable(false)
        , base_(base)
        , table_(table)
        , evaluated_table_()
        , debugger_(fdb)
    {
    }

private:
    const formula_callable& base_;
    expr_table_ptr table_;
    mutable expr_table_evaluated evaluated_table_;
    formula_debugger* debugger_;

    void get_inputs(formula_input_vector& inputs) const
    {
        for(expr_table::const_iterator i = table_->begin(); i != table_->end(); ++i) {
            add_input(inputs, i->first);
        }
    }

    variant get_value(const std::string& key) const
    {
        expr_table::iterator i = table_->find(key);
        if(i != table_->end()) {
            expr_table_evaluated::const_iterator ev = evaluated_table_.find(key);
            if(ev != evaluated_table_.end()) {
                return ev->second;
            }

            variant v = i->second->evaluate(base_, add_debug_info(debugger_, 0, "where[" + key + "]"));
            evaluated_table_[key] = v;
            return v;
        }

        return base_.query_value(key);
    }
};

class where_expression: public formula_expression
{
public:
    where_expression(expression_ptr body, expr_table_ptr clauses)
        : body_(body), clauses_(clauses)
    {}

    std::string str() const
    {
        std::stringstream s;
        s << "{where:(";
        s << body_->str();
        for(const expr_table::value_type &a : *clauses_) {
            s << ", [" << a.first << "] -> ["<< a.second->str()<<"]";
        }
        s << ")}";
        return s.str();
    }

private:
    expression_ptr body_;
    expr_table_ptr clauses_;

    variant execute(const formula_callable& variables,formula_debugger*fdb) const
    {
        where_variables wrapped_variables(variables, clauses_, fdb);
        return body_->evaluate(wrapped_variables, add_debug_info(fdb, 0, "... where"));
    }
};


class identifier_expression : public formula_expression
{
public:
    explicit identifier_expression(const std::string& id) : id_(id) {}

    std::string str() const
    {
        return id_;
    }

private:
    variant execute(const formula_callable& variables, formula_debugger* /*fdb*/) const
    {
        return variables.query_value(id_);
    }

    std::string id_;
};

class integer_expression : public formula_expression
{
public:
    explicit integer_expression(int i) : i_(i) {}

    std::string str() const
    {
        std::stringstream s;
        s << i_;
        return s.str();
    }

private:
    variant execute(const formula_callable& /*variables*/, formula_debugger* /*fdb*/) const
    {
        return variant(i_);
    }

    int i_;
};

class decimal_expression : public formula_expression
{
public:
    decimal_expression(int i, int f) : i_(i), f_(f) {}

    std::string str() const
    {
        std::stringstream s;
        s << i_ << '.';
        s.width(3);
        s.fill('0');
        s << f_;
        return s.str();
    }

private:
    variant execute(const formula_callable& /*variables*/, formula_debugger* /*fdb*/) const
    {
        return variant(i_ * 1000 + f_, variant::DECIMAL_VARIANT );
    }

    int i_, f_;
};

class string_expression : public formula_expression
{
public:
    explicit string_expression(std::string str)
        : str_()
        , subs_()
    {
        std::string::iterator i = str.begin();
        while((i = std::find(i, str.end(), '[')) != str.end()) {
            int bracket_depth = 0;
            std::string::iterator j = i + 1;
            while(j != str.end() && (bracket_depth > 0 || *j != ']')) {
                if(*j == '[') {
                    bracket_depth++;
                } else if(*j == ']' && bracket_depth > 0) {
                    bracket_depth--;
                }
                ++j;
            }

            if(j == str.end()) {
                break;
            }

            const std::string formula_str(i+1, j);
            const int pos = std::distance(str.begin(), i);
            if(j - i == 2 && (i[1] == '(' || i[1] == '\'' || i[1] == ')')) {
                // Bracket contained nothing but a quote or parenthesis.
                // This means it was intended as a literal quote or square bracket.
                i = str.erase(i);
                if(*i == '(') {
                    *i = '[';
                } else if(*i == ')') {
                    *i = ']';
                }

                i = str.erase(i + 1);
                continue;
            } else {
                i = str.erase(i, j+1);
            }

            substitution sub;
            sub.pos = pos;
            try {
                sub.calculation.reset(new formula(formula_str));
            } catch(formula_error& e) {
                e.filename += " - string substitution";
                throw;
            }

            subs_.push_back(sub);
        }

        std::reverse(subs_.begin(), subs_.end());

        str_ = variant(str);
    }

    std::string str() const
    {
        std::string res = str_.as_string();
        int j = res.size() - 1;

        for(const auto& sub : subs_) {
            for(; j >= sub.pos && j >= 0; j--) {
                if(res[j] == '\'') {
                    res.replace(j, 1, "[']");
                } else if(res[j] == '[') {
                    res.replace(j, 1, "[(]");
                } else if(res[j] == ']') {
                    res.replace(j, 1, "[)]");
                }
            }

            const std::string str = "[" + sub.calculation->str() + "]";
            res.insert(sub.pos, str);
        }

        for(; j >= 0; j--) {
            if(res[j] == '\'') {
                res.replace(j, 1, "[']");
            } else if(res[j] == '[') {
                res.replace(j, 1, "[(]");
            } else if(res[j] == ']') {
                res.replace(j, 1, "[)]");
            }
        }

        return "'" + res + "'";
    }

private:
    variant execute(const formula_callable& variables, formula_debugger*fdb) const
    {
        if(subs_.empty()) {
            return str_;
        }

        std::string res = str_.as_string();
        for(std::size_t i = 0; i < subs_.size(); ++i) {
            const int j = subs_.size() - i - 1;
            const substitution& sub = subs_[i];
            add_debug_info(fdb, j, "[string subst]");
            const std::string str = sub.calculation->evaluate(variables,fdb).string_cast();
            res.insert(sub.pos, str);
        }

        return variant(res);
    }

    struct substitution
    {
        substitution() : pos(0) , calculation() {}

        int pos;
        const_formula_ptr calculation;
    };

    variant str_;
    std::vector<substitution> subs_;
};


/**
 * Functions to handle the actual parsing of WFL.
 */
static int operator_precedence(const tk::token& t)
{
    static std::map<std::string,int> precedence_map;
    if(precedence_map.empty()) {
        int n = 0;
        precedence_map["not"]   = ++n;
        precedence_map["where"] = ++n;
        precedence_map["or"]    = ++n;
        precedence_map["and"]   = ++n;
        precedence_map["="]     = ++n;
        precedence_map["!="]    = n;
        precedence_map["<"]     = n;
        precedence_map[">"]     = n;
        precedence_map["<="]    = n;
        precedence_map[">="]    = n;
        precedence_map["in"]    = n;
        precedence_map["~"]     = ++n;
        precedence_map["+"]     = ++n;
        precedence_map["-"]     = n;
        precedence_map[".."]    = n;
        precedence_map["*"]     = ++n;
        precedence_map["/"]     = n;
        precedence_map["%"]     = ++n;
        precedence_map["^"]     = ++n;
        precedence_map["d"]     = ++n;
        precedence_map["."]     = ++n;
    }

    assert(precedence_map.count(std::string(t.begin, t.end)));
    return precedence_map[std::string(t.begin, t.end)];
}

static void parse_function_args(const tk::token* &i1, const tk::token* i2, std::vector<std::string>* res)
{
    const tk::token* begin = i1, *end = i2; // These are used for error reporting

    if(i1->type == tk::TOKEN_LPARENS) {
        ++i1;
    } else {
        throw formula_error("Invalid function definition", tokens_to_string(begin,end - 1), *i1->filename, i1->line_number);
    }

    while((i1-> type != tk::TOKEN_RPARENS) && (i1 != i2)) {
        if(i1->type == tk::TOKEN_IDENTIFIER) {
            if(std::string((i1+1)->begin, (i1+1)->end) == "*") {
                res->push_back(std::string(i1->begin, i1->end) + std::string("*"));
                ++i1;
            } else {
                res->push_back(std::string(i1->begin, i1->end));
            }
        } else if(i1->type == tk::TOKEN_COMMA) {
            //do nothing
        } else {
            throw formula_error("Invalid function definition", tokens_to_string(begin,end - 1), *i1->filename, i1->line_number);
        }

        ++i1;
    }

    if(i1->type != tk::TOKEN_RPARENS) {
        throw formula_error("Invalid function definition", tokens_to_string(begin,end - 1), *i1->filename, i1->line_number);
    }

    ++i1;
}

static void parse_args(const tk::token* i1, const tk::token* i2,
                std::vector<expression_ptr>* res,
                function_symbol_table* symbols)
{
    int parens = 0;
    const tk::token* beg = i1;
    while(i1 != i2) {
        if(i1->type == tk::TOKEN_LPARENS || i1->type == tk::TOKEN_LSQUARE ) {
            ++parens;
        } else if(i1->type == tk::TOKEN_RPARENS || i1->type == tk::TOKEN_RSQUARE ) {
            --parens;
        } else if(i1->type == tk::TOKEN_COMMA && !parens) {
            res->push_back(parse_expression(beg, i1, symbols));
            beg = i1+1;
        }

        ++i1;
    }

    if(beg != i1) {
        res->push_back(parse_expression(beg, i1, symbols));
    }
}

static void parse_set_args(const tk::token* i1, const tk::token* i2,
                std::vector<expression_ptr>* res,
                function_symbol_table* symbols)
{
    int parens = 0;
    bool check_pointer = false;
    const tk::token* beg = i1;
    const tk::token* begin = i1, *end = i2; // These are used for error reporting
    while(i1 != i2) {
        if(i1->type == tk::TOKEN_LPARENS || i1->type == tk::TOKEN_LSQUARE) {
            ++parens;
        } else if(i1->type == tk::TOKEN_RPARENS || i1->type == tk::TOKEN_RSQUARE) {
            --parens;
        } else if(i1->type == tk::TOKEN_POINTER && !parens ) {
            if(!check_pointer) {
                check_pointer = true;
                res->push_back(parse_expression(beg, i1, symbols));
                beg = i1+1;
            } else {
                throw formula_error("Too many '->' operators found", tokens_to_string(begin,end - 1), *i1->filename, i1->line_number);
            }
        } else if(i1->type == tk::TOKEN_COMMA && !parens ) {
            if(check_pointer)
                check_pointer = false;
            else {
                throw formula_error("Expected comma, but '->' found", tokens_to_string(begin,end - 1), *i1->filename, i1->line_number);
            }
            res->push_back(parse_expression(beg, i1, symbols));
            beg = i1+1;
        }

        ++i1;
    }

    if(beg != i1) {
        res->push_back(parse_expression(beg, i1, symbols));
    }
}

static void parse_where_clauses(const tk::token* i1, const tk::token* i2, expr_table_ptr res, function_symbol_table* symbols)
{
    int parens = 0;
    const tk::token* original_i1_cached = i1;
    const tk::token* beg = i1;
    const tk::token* begin = i1, *end = i2; // These are used for error reporting
    std::string var_name;

    while(i1 != i2) {
        if(i1->type == tk::TOKEN_LPARENS || i1->type == tk::TOKEN_LSQUARE) {
            ++parens;
        } else if(i1->type == tk::TOKEN_RPARENS || i1->type == tk::TOKEN_RSQUARE) {
            --parens;
        } else if(!parens) {
            if(i1->type == tk::TOKEN_COMMA) {
                if(var_name.empty()) {
                    throw formula_error("There is 'where <expression>' but 'where name=<expression>' was needed",
                        tokens_to_string(begin, end - 1), *i1->filename, i1->line_number);
                }

                (*res)[var_name] = parse_expression(beg, i1, symbols);
                beg = i1+1;
                var_name = "";
            } else if(i1->type == tk::TOKEN_OPERATOR) {
                std::string op_name(i1->begin, i1->end);

                if(op_name == "=") {
                    if(beg->type != tk::TOKEN_IDENTIFIER) {
                        if(i1 == original_i1_cached) {
                            throw formula_error("There is 'where <expression>' but 'where name=<expression>' was needed",
                                tokens_to_string(begin, end - 1), *i1->filename, i1->line_number);
                        } else {
                            throw formula_error("There is 'where <expression>=<expression>' but 'where name=<expression>' was needed",
                                tokens_to_string(begin, end - 1), *i1->filename, i1->line_number);
                        }
                    } else if(beg+1 != i1) {
                        throw formula_error("There is 'where name <expression>=<expression>' but 'where name=<expression>' was needed",
                            tokens_to_string(begin, end - 1), *i1->filename, i1->line_number);
                    } else if(!var_name.empty()) {
                        throw formula_error("There is 'where name=name=<expression>' but 'where name=<expression>' was needed",
                            tokens_to_string(begin, end - 1), *i1->filename, i1->line_number);
                    }

                    var_name.insert(var_name.end(), beg->begin, beg->end);
                    beg = i1+1;
                }
            }
        }
        ++i1;
    }

    if(beg != i1) {
        if(var_name.empty()) {
            throw formula_error("There is 'where <expression>' but 'where name=<expression>' was needed",
                tokens_to_string(begin, end - 1), *i1->filename, i1->line_number);
        }

        (*res)[var_name] = parse_expression(beg, i1, symbols);
    }
}

expression_ptr parse_expression(const tk::token* i1, const tk::token* i2, function_symbol_table* symbols)
{
    if(i1 == i2) {
        throw formula_error("Empty expression", "", *i1->filename, i1->line_number);
    }

    std::unique_ptr<function_symbol_table> temp_functions;
    if(!symbols) {
        temp_functions.reset(new function_symbol_table(function_symbol_table::get_builtins()));
        symbols = temp_functions.get();
    }

    const tk::token* begin = i1, *end = i2; // These are used for error reporting

    if(i1->type == tk::TOKEN_KEYWORD && (i1 + 1)->type == tk::TOKEN_IDENTIFIER) {
        if(std::string(i1->begin, i1->end) == "def") {
            ++i1;
            const std::string formula_name = std::string(i1->begin, i1->end);

            std::vector<std::string> args;
            parse_function_args(++i1, i2, &args);

            const tk::token* beg = i1;
            while((i1 != i2) && (i1->type != tk::TOKEN_SEMICOLON)) {
                ++i1;
            }

            const std::string precond = "";
            if(symbols == nullptr) {
                throw formula_error("Function symbol table required but not present", "",*i1->filename, i1->line_number);
            }

            symbols->add_function(formula_name,
                std::make_shared<user_formula_function>(
                    formula_name, std::make_shared<const formula>(beg, i1, symbols),
                    formula::create_optional_formula(precond, symbols), args
                )
            );

            if((i1 == i2) || (i1 == (i2-1))) {
                return std::make_shared<function_list_expression>(symbols);
            } else {
                return parse_expression((i1+1), i2, symbols);
            }
        }
    }

    int parens = 0;
    const tk::token* op = nullptr;
    bool operator_group = false;

    for(const tk::token* i = i1; i != i2; ++i) {
        if(i->type == tk::TOKEN_LPARENS || i->type == tk::TOKEN_LSQUARE) {
            ++parens;
        } else if(i->type == tk::TOKEN_RPARENS || i->type == tk::TOKEN_RSQUARE) {
            --parens;
        } else if(parens == 0 && i->type == tk::TOKEN_OPERATOR) {
            if((!operator_group ) && (op == nullptr || operator_precedence(*op) >= operator_precedence(*i))) {
                // Need special exception for exponentiation to be right-associative
                if(*i->begin != '^' || op == nullptr || *op->begin != '^') {
                    op = i;
                }
            }
            operator_group = true;
        } else {
            operator_group = false;
        }
    }

    if(op == nullptr) {
        if(i1->type == tk::TOKEN_LPARENS && (i2-1)->type == tk::TOKEN_RPARENS) {
            return parse_expression(i1+1,i2-1,symbols);
        } else if((i2-1)->type == tk::TOKEN_RSQUARE) { //check if there is [ ] : either a list/map definition, or a operator
            // First, a special case for an empty map
            if(i2 - i1 == 3 && i1->type == tk::TOKEN_LSQUARE && (i1+1)->type == tk::TOKEN_POINTER) {
                return std::make_shared<map_expression>(std::vector<expression_ptr>());
            }

            const tk::token* tok = i2-2;
            int square_parens = 0;
            bool is_map = false;
            while ((tok->type != tk::TOKEN_LSQUARE || square_parens) && tok != i1) {
                if(tok->type == tk::TOKEN_RSQUARE) {
                    square_parens++;
                } else if(tok->type == tk::TOKEN_LSQUARE) {
                    square_parens--;
                } else if((tok->type == tk::TOKEN_POINTER) && !square_parens ) {
                    is_map = true;
                }
                --tok;
            }

            if(tok->type == tk::TOKEN_LSQUARE) {
                if(tok == i1) {
                    // Create a list or a map
                    std::vector<expression_ptr> args;

                    if( is_map ) {
                        parse_set_args(i1+1, i2-1, &args, symbols);
                        return std::make_shared<map_expression>(args);
                    } else {
                        parse_args(i1+1,i2-1,&args,symbols);
                        return std::make_shared<list_expression>(args);
                    }
                } else {
                    // Execute operator [ ]
                    try{
                        return std::make_shared<square_bracket_expression>(
                            parse_expression(i1,      tok,    symbols),
                            parse_expression(tok + 1, i2 - 1, symbols)
                        );
                    } catch (const formula_error& e){
                        throw formula_error( e.type, tokens_to_string(i1, i2-1), *i1->filename, i1->line_number );
                    }
                }
            }
        } else if(i2 - i1 == 1) {
            if(i1->type == tk::TOKEN_KEYWORD) {
                if(std::string(i1->begin, i1->end) == "functions") {
                    return std::make_shared<function_list_expression>(symbols);
                }
            } else if(i1->type == tk::TOKEN_IDENTIFIER) {
                return std::make_shared<identifier_expression>(std::string(i1->begin, i1->end));
            } else if(i1->type == tk::TOKEN_INTEGER) {
                int n = std::stoi(std::string(i1->begin, i1->end));
                return std::make_shared<integer_expression>(n);
            } else if(i1->type == tk::TOKEN_DECIMAL) {
                tk::iterator dot = i1->begin;
                while(*dot != '.') {
                    ++dot;
                }

                int n = std::stoi(std::string(i1->begin,dot));

                tk::iterator literal_end = i1->end;

                if(literal_end - dot > 4) {
                   literal_end = dot + 4;
                }

                ++dot;

                int f = 0;

                int multiplicator = 100;
                while(dot != literal_end) {
                    f += (*dot - 48) * multiplicator;
                    multiplicator /= 10;
                    ++dot;
                }

                return std::make_shared<decimal_expression>(n, f);
            } else if(i1->type == tk::TOKEN_STRING_LITERAL) {
                return std::make_shared<string_expression>(std::string(i1->begin + 1, i1->end - 1));
            }
        } else if(i1->type == tk::TOKEN_IDENTIFIER &&
                  (i1+1)->type == tk::TOKEN_LPARENS &&
                  (i2-1)->type == tk::TOKEN_RPARENS)
        {
            const tk::token* function_call_begin = i1, *function_call_end = i2; // These are used for error reporting
            int nleft = 0, nright = 0;
            for(const tk::token* i = i1; i != i2; ++i) {
                if(i->type == tk::TOKEN_LPARENS) {
                    ++nleft;
                } else if(i->type == tk::TOKEN_RPARENS) {
                    ++nright;
                }
            }

            if(nleft == nright) {
                std::vector<expression_ptr> args;
                parse_args(i1+2,i2-1,&args,symbols);
                try{
                    return symbols->create_function(std::string(i1->begin, i1->end),args);
                }
                catch(const formula_error& e) {
                    throw formula_error(e.type, tokens_to_string(function_call_begin, function_call_end), *i1->filename, i1->line_number);
                }
            }
        }

        throw formula_error("Could not parse expression", tokens_to_string(i1, i2), *i1->filename, i1->line_number);
    }

    if(op + 1 == end) {
        throw formula_error("Expected another token", tokens_to_string(begin, end - 1), *op->filename, op->line_number);
    }

    if(op == i1) {
        try{
            return expression_ptr(
                new unary_operator_expression(std::string(op->begin, op->end), parse_expression(op + 1, i2 ,symbols)));
        } catch(const formula_error& e) {
            throw formula_error( e.type, tokens_to_string(begin,end - 1), *op->filename, op->line_number);
        }
    }

    const std::string op_name(op->begin,op->end);

    if(op_name == ".") {
        return expression_ptr(
            new dot_expression(
                parse_expression(i1,    op, symbols),
                parse_expression(op + 1,i2, symbols)
            )
        );
    }

    if(op_name == "where") {
        expr_table_ptr table(new expr_table());
        parse_where_clauses(op+1, i2, table, symbols);

        return std::make_shared<where_expression>(parse_expression(i1, op, symbols), table);
    }

    return expression_ptr(
        new operator_expression(op_name,
            parse_expression(i1,     op, symbols),
            parse_expression(op + 1, i2, symbols)
        )
    );
}

} // namespace wfl